Saudi Arabia launched a war against the Houthis in March 2015, after the rebels drove Yemen's internationally recognised government from the capital, Sanaa.
United Nations chief Antonio Guterres met Yemen's foreign minister at the United Nations headquarters in NY on Monday.
He also played a video that showed the destruction of Houthi capabilities in Yemen such as destroying a missile launcher in Saada and a factory to manufacture drones in Hajjah and targeting Houthis in Al-Jawf axis. "I hope that it will be possible to avoid a battle for Hodeidah".
The United Nations warned Friday that a military attack or siege on Hodeida would affect hundreds of thousands of civilians.
With the failure of diplomatic efforts, the clock is now ticking to the launch of a military offensive to liberate the port city.
"Our message is clear. if this assault happens then it would be very hard to imagine how hard the situation the people in Yemen, particularly in Hodeidah, will be in", said Muhsin Siddiqui, country director of Oxfam.
Militarily, one source predicted that "a wider campaign that involves serious coalition firepower ... makes it unlikely that the Houthis will be able to hold the city or its port for more than a few weeks".
The source, based in Hodeidah, pointed out that ferocious armed confrontations are now underway in different areas near the city's main entrances.
Urban battles, however, will jeopardise civilian lives and risk bogging down assault forces. Turki al-Malki as announcing the deaths Saturday in Jizan province.
Yemen's minister of human rights Mohamad Askar summed up the dilemma.
Clashes between the military and Houthi rebel forces intensified last week, as troops led by the UAE advanced to 10 km (6 miles) from the city, Reuters reported.
Britain has urged the UAE not to press ahead with an assault on Yemen's main port following United Nations warnings that the attack could leave hundreds of thousands dead in a country already on the brink of starvation.